Question

The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs.405. What was the rate of interest?

• A. 15 $\%$
• B. 16 $\%$
• C. 17 $\%$
• D. 18 $\%$

Answer 1

The correct option is A

15 $\%$

Let the rate be $R\%$ p.a. Then,
$\left[18000\right(1+\frac{R}{100}{)}^2-18000]-\left(\frac{18000\times R\times 2}{100}\right)=405$.
$⟺18000[\frac{(100+R{)}^2}{10000}-1-\frac{2R}{100}]=405$
$⟺18000\left[\frac{(100+R{)}^2-10000-200R)}{10000}\right]=405$
$⟺\frac{9}{5}{R}^2=405⟺R^2=\left(\frac{405\times 5}{9}\right)=225⟺R=15$.
$\therefore Rate=15\%$.